Question

The table shows the 2009 estimated populations and gross domestic products (GDP) for several countries, given in scientific notation. Find the per capita GDP for each country. (Round your answers to two decimal places.)

Germany (population) 8.23 × 10^7 (GDP in US Dollars) 2.81 × 10^12

Iceland (population) 4.58 × 10^6 (GDP in US Dollars) 1.77 × 10^11

I've tried evaluating the pop and GDP by multiplying, dividing and rounding but I still am not getting the right answer, please help. Thanks.

Answer 1

"Per capita" is latin for "per head" which essentially tells you what the average income is per person

http://en.wikipedia.org/wiki/Per_capita

So if the entire country of 10 people makes a total of $1000 a year, then each person is making on average 1000/10 = 100 dollars a year

Answer 2

So you just divide the total GDP of that country by its population (GDP/population) to get the per capita GDP

Answer 3

@jim_thompson5910 Like I said before. I've already divided, multiplied and tried many things. Even I divided the GDP and population. Still the wrong answer. The rest of the answers were correct. I don't know about this one. Sorry.

Answer 4

When you divided, what did you get?

Answer 5

I first divided Germany's GDP/Pop. 2.81 x 10^12 / 8.23 x 10^7
The answer I got was 0.34 x 10^5

I did the same thing with Iceland and got 0.39 x 10^5

Answer 6

@jim_thompson5910

Answer 7

is 0.34 x 10^5 in scientific notation?

Answer 8

Yes, the answers are in scientific notation, unless if I was missing something.

Answer 9

0.34 x 10^5 is not in scientific notation

Answer 10

the base 0.34 throws it off

Answer 11

for a number to be in scientific notation, the base has to be between 1 and 10 (including 1, but excluding 10)

Answer 12

Oh..same format I meant, but I had no clue about the 0.39 and 0.34. How do I fix this?

Answer 13

0.34 is equal to 3.4 x 10^(-1)

notice how the 3.4 turns into 0.34 after you move the decimal point 1 spot to the left. So that's why the exponent is -1

Answer 14

So we have this transformation

0.34 x 10^5

( 3.4 x 10^-1) x 10^5

3.4 x (10^-1 x 10^5)

3.4 x 10^(-1 + 5)

3.4 x 10^4

Answer 15

That work shows 0.34 x 10^5 is equal to 3.4 x 10^4

the base 3.4 is now between 1 and 10, so the number is in scientific notation now

Answer 16

That makes so much sense now. I'll keep this step in mind for future problems like this. I appreciate your help. Thank you!

Answer 17

you're welcome